DOCSLIB.ORG

Bridging the Gap Between Ecological Diversity Indices and Measures of Biodiversity with Shannon’S Entropy: Comment to Izsa´K and Papp

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Bridging the Gap Between Ecological Diversity Indices and Measures of Biodiversity with Shannon’S Entropy: Comment to Izsa´K and Papp Ecological Modelling 152 (2002) 1–3 www.elsevier.com/locate/ecolmodel Bridging the gap between ecological diversity indices and measures of biodiversity with Shannon’s entropy: comment to Izsa´k and Papp Carlo Ricotta * Department of Plant Biology, Uni6ersity of Rome ‘‘La Sapienza’’, Piazzale Aldo Moro 5, 00185 Rome, Italy Received 31 May 2001; accepted 11 October 2001 Abstract Most ecological diversity indices summarize the information about the relative abundances of community species without reflecting taxonomic differences between species. Nevertheless, in the environmental conservation practice, data on species abundances are generally unknown. In such cases, to summarize the conservation value of a given site, so-called ‘biological diversity’ measures need to be used. Most of these measures are based on taxonomic relations among species and ignore species relative abundances. In a recent paper, Izsa´k and Papp suggest that the quadratic entropy index (Q) is the only diversity index used to date in the ecological practice that incorporates both species relative abundances and a measure of the pairwise taxonomic differences between species in the analyzed data set. I show here that a number of traditional ecological diversity measures can be generalized to take into account a taxonomic weighting factor. Since these new indices violate part of the mathematical properties that an index should meet to be termed an ecological diversity index, I defined this new family of indices ‘weak diversity indices’. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Biodiversity measures; Ecological diversity; Quadratic entropy; Shannon’s entropy; Species richness 1. Introduction data on species abundances are generally un- known. Often the only available data is the num- Traditional ecological diversity indices, such as ber of species. For instance, focusing on the Shannon index and the Simpson index, sum- conservation problems, species abundances are marize the information about the relative abun- mostly irrelevant. In addition, the comparison of dances of species within a species sample or species abundances is largely meaningless between community without regard to species names or systematically remote organisms, such as oaks differences between species. Nevertheless, for and orchids (Izsa´k and Papp, 2000). large-scale environmental protection purposes, In these circumstances, to summarize the con- servation value of a given site, so-called ‘biologi- * Tel.: +39-06-4991-2408; fax: +39-06-4457-540. cal diversity’ measures are generally preferred. E-mail address: [email protected] (C. Ricotta). Most of these measures are based on taxonomic 0304-3800/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S0304-3800(01)00468-9 2 C. Ricotta / Ecological Modelling 152 (2002) 1–3 relations among species and are not linked to number of edges) between the i-th and the j-th traditional diversity indices. To our knowledge, species in the taxonomic tree. An illustration of an Vane-Wright et al. (1991) were the first to suggest artificial taxonomic tree along with its species that, for conservation purposes, we should quantify distance matrix is given in Fig. 1. For example, in the ‘taxonomic distinctiveness’ of different species. Fig. 1, the taxonomic distance dac from species a to For a given data set, Vane-Wright et al. (1991) species c is 4. proposed a measure of the degree of ‘independent If the species abundance values are unknown (i.e. evolutionary history’ that takes into account the if the only available data is species richness), we can topology of the corresponding taxonomic tree, but attribute the same abundance value 1/N to all ignores species relative abundances. Successively, species present. In this case, Eq. (1) expresses the various refinements of this basic idea have been mean taxonomic distance between two randomly actively pursued (Faith, 1992, 1995). In this view, selected species and can be written in the form: Izsa´k and Papp (2000) suggest that the quadratic N N 1 % % entropy index (Rao, 1982) is the only ecological J= 2 dij. (2) diversity index used to date in the ecological N i=1j=1 practice that incorporates both species relative Izsa´k and Papp (2000) note that J does not satisfy abundances and a measure of the pairwise taxo- set monotonicity, a property generally required for nomic differences between species in the analyzed biodiversity measures. This property ensures that data set. the index value will increase by adding a new Consider an N-species community characterized species to a species set A. Formally, denoting a @ \ by the relative abundance vector P=(p1, p2,…, pN) biodiversity index by I, I(A {x}) I(N). Con- 0 0 N such that such that 0 pi 1 and i=1pi =1. Rao versely, the extensive counterpart of J: (1982) defined the quadratic diversity index Q or N N 2 % % quadratic entropy as: F=N J= dij, (3) i=1j=1 N N % % Q= dij pi pj, (1) where F is the sum of the taxonomic differences of i=1j=1 species in the analyzed data set satisfy set where dij is the difference between the i-th and the monotonicity. F is therefore an adequate measure j-th species (dij =dji and dii =0) and Q expresses the of biodiversity if data on species relative abun- average difference between two randomly selected dances are unknown (Izsa´k and Papp, 2000). No- individuals. It is easily shown that for dij =constant tice that F is not simply a (species) richness index " for all i j, Q reduces to dij(1−D), where D is the insofar as it is not a monotone increasing function N 2 Simpson index i=1p i . To apply Q in practice, the of the number of species in the data set. Instead, differences dij need to be specified. Izsa´k and Papp its values are jointly determined by the number of (2000) propose to generate species differences based species and the (taxonomic) differences between the on the taxonomic distance between two species, let species (Izsa´k and Papp, 2000). dij stand for the topological distance (i.e. the 2. Linking ecological diversity and biodiversity with Shannon’s entropy In a similar manner, it is also possible to bridge the gap between traditional ecological diversity indices based on species relative abundances and conservation-oriented biodiversity indices starting N Fig. 1. Illustration of an artificial taxonomic tree along with its from Shannon’s entropy H=− i=1pi log pi. species distance matrix to clarify how to measure taxonomic Shannon’s entropy H of a given community is a distances. information-theoretic measure of uncertainty in C. Ricotta / Ecological Modelling 152 (2002) 1–3 3 % % % predicting the relative abundance of species. Since p2,…, pN andtoap 1, p 2,…, p N permutation of those uncertainty is maximal when entropy is highest, are identical. Therefore, I propose to define these information theory forms one of the basic founda- indices that derive from traditional ecological di- tions of ecological diversity theory (Orlo´ci, 1991). versity indices but that have their greatest value for Within this framework, Casquilho et al. (1998) non-completely even communities ‘weak diversity proposed a generalized version of Shannon’s en- indices’. Notice that the weak diversity formulation tropy of Shannon’s entropy reported in Eq. (4) can be N easily extended to parametric diversity indices such % D HG =− wi pi log pi, (4) as the i diversity family (Patil and Taillie, 1982) i=1 1 D N i i = i=1wi pi(1−p i )ortoAcze´l and Daro´czy where wi is a weighting factor that embodies the i ‘quality’ of the i-th species in the data set. Based h 1 (1975) generalized entropy H = on the species distance matrix of Fig. 1, a simple 21−h −1 N h way to compute a taxonomic weight wi associated i=1wi(p i −pi) to obtain a vector representation of to the i-th species in the data set is to add all dij community diversity as suggested by Patil and elements along row i or column i of the species Taillie (1982). Will weak diversity indices be able matrix. The result of this summation represents the to effectively summarize the important information total taxonomic distance from the i-th species to all contained in the analyzed species assemblages? This other species in the data set. For example, in Fig. is a critical question and their answer will provide 1, the taxonomic weight wa associated to species a valuable insights into the practice of nature conser- is 18. vation. If the species abundance values are unknown, two expression analogous to J and F can be derived (see Eqs. (2) and (3)): References N 1 % Acze´l, J., Daro´czy, Z., 1975. On Measures of Information and JG = wi log N (5) their Characterizations. Academic Press, New York. Ni=1 Casquilho, J., Neves, M., Rego, F., 1998. Extenso˜es da func¸a˜o and de Shannon e equil´ıbrios de proporc¸o˜es—uma aplicac¸a˜oao mosaico de paisagem. Anais do Instituto Superior de Agro- N % nomia 48, 77–99. FG =NJG =log N wi, (6) i=1 Faith, D.P., 1992. Conservation evaluation and phylogenic diversity. Biol. Conserv. 61, 1–10. N N N where i=1wi = i=1 j=1dij and log N is the en- Faith, D.P., 1995. Phylogenic pattern and the quantification of tropy introduced by Hartley (1928), who wanted organismal biodiversity. In: Hawksworth, D.L. (Ed.), Biodi- the entropy to depend only upon the number of versity Measurement and Estimation. Chapman & Hall, species, not upon their relative abundances. There- London, pp. 45–58. Hartley, R.V., 1928. Transmission of information. Bell Syst. fore, since FG takes into account species richness Techn.
Load more

Recommended publications
  • Species Biodiversity Lab
    SCIENCE IN THE PARK: ROCK POOLS SPECIES BIODIVERSITY LAB Purpose: To understand the importance of biodiversity, calculate the indices of the Simpson’s Index, and quantify the biodiversity of a sample. Developed by E. A. Betts Time: 40 minutes BACKGROUND: Simpson's Diversity Index is a measure of diversity. In ecology, it is often used to quantify the biodiversity of a habitat. It takes into account the number of species present, as well as the abundance of each species. Before looking at Simpson's Diversity Index in more detail, it is important to understand the basic concepts. Biological diversity can be quantified in many different ways. The two main factors taken into account when measuring diversity are richness and evenness. Richness is a measure of the number of different kinds of organisms present in a particular area. For example, species richness is the number of different species present. However, diversity depends not only on richness, but also on evenness. Evenness compares the similarity of the population size of each of the species present. Richness - The number of species per sample is a measure of richness. The more species present in a sample, the 'richer' the sample. Species richness as a measure on its own takes no account of the number of individuals of each species present. It gives as much weight to those species which have very few individuals as to those which have many individuals. Thus, one daisy has as much influence on the richness of an area as 1000 buttercups. Evenness - Evenness is a measure of the relative abundance of the different species that make up the richness of an area.
    [Show full text]
  • Indexes of Group Diversity 1 Some Common Indexes Of
    INDEXES OF GROUP DIVERSITY 1 SOME COMMON INDEXES OF GROUP DIVERSITY: UPPER BOUNDARIES1,2 ANTONIO SOLANAS Department of Behavioral Sciences Methods, Faculty of Psychology, University of Barcelona Institute for Research in Brain, Cognition, and Behavior (IR3C), University of Barcelona REJINA M. SELVAM Department of Behavioral Sciences Methods, Faculty of Psychology, University of Barcelona Institute for Research in Brain, Cognition, and Behavior (IR3C), University of Barcelona JOSÉ NAVARRO Department of Social Psychology, Faculty of Psychology, University of Barcelona DAVID LEIVA Department of Behavioral Sciences Methods, Faculty of Psychology, University of Barcelona Institute for Research in Brain, Cognition, and Behavior (IR3C), University of Barcelona 1 Address correspondence to Antonio Solanas, Departament de Metodologia de les Ciències del Comportament, Facultat de Psicologia, Universitat de Barcelona, Passeig de la Vall d’Hebron, 171, 08035-Barcelona, Spain. Electronic mail may be sent to Antonio Solanas at: ([email protected]) 2This research was supported by the Spanish Ministry of Science and Innovation, grant PSI2009-07076 and by the Generalitat of Catalonia’s Agència de Gestió d’Ajuts Universitaris i de Recerca, grant 2009SGR1492. INDEXES OF GROUP DIVERSITY 2 Summary. —Workgroup diversity can be conceptualized as variety, separation, or disparity. Thus, the proper operationalization of diversity depends on how a diversity dimension has been defined. Analytically, the minimal diversity must be obtained when there are no differences
    [Show full text]
  • Diversity Indices: Shannon and Simpson
    Name: Date: Student Handout 1A: How to Calculate Biodiversity Diversity Indices: A) A diversity index is a mathematical measure of species diversity in a given community. B) Based on the species richness (the number of species present) and species abundance (the number of individuals per species). C) The more species you have, the more diverse the area, right? D) However, there are two types of indices, dominance indices and information statistic indices. E) The equations for the two indices we will study are: s Shannon Index (H) = - ∑ pi ln pi i=1 1 Simpson Index (D) = s 2 ∑ pi i=1 The Shannon index is an information statistic index, which means it assumes all species are represented in a sample and that they are randomly sampled. Can you point out any problems in these assumptions? In the Shannon index, p is the proportion (n/N) of individuals of one particular species found (n) divided by the total number of individuals found (N), ln is the natural log, Σ is the sum of the calculations, and s is the number of species. The Simpson index is a dominance index because it gives more weight to common or dominant species. In this case, a few rare species with only a few representatives will not affect the diversity. Can you point out any problems in these assumptions? In the Simpson index, p is the proportion (n/N) of individuals of one particular species found (n) divided by the total number of individuals found (N), Σ is still the sum of the calculations, and s is the number of species.
    [Show full text]
  • The Shannon-Weiner Species Diversity Index
    This article reprinted from: Nolan, K.A. and J.E. Callahan. 2006. Beachcomber biology: The Shannon-Weiner Species Diversity Index. Pages 334-338, in Tested Studies for Laboratory Teaching, Volume 27 (M.A. O'Donnell, Editor). Proceedings of the 27th Workshop/Conference of the Association for Biology Laboratory Education (ABLE), 383 pages. Compilation copyright © 2006 by the Association for Biology Laboratory Education (ABLE) ISBN 1-890444-09-X All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the copyright owner. Use solely at one’s own institution with no intent for profit is excluded from the preceding copyright restriction, unless otherwise noted on the copyright notice of the individual chapter in this volume. Proper credit to this publication must be included in your laboratory outline for each use; a sample citation is given above. Upon obtaining permission or with the “sole use at one’s own institution” exclusion, ABLE strongly encourages individuals to use the exercises in this proceedings volume in their teaching program. Although the laboratory exercises in this proceedings volume have been tested and due consideration has been given to safety, individuals performing these exercises must assume all responsibilities for risk. The Association for Biology Laboratory Education (ABLE) disclaims any liability with regards to safety in connection with the use of the exercises in this volume. The focus of ABLE is to improve the undergraduate biology laboratory experience by promoting the development and dissemination of interesting, innovative, and reliable laboratory exercises.
    [Show full text]
  • Spatial Patterns of Bacterial Richness and Evenness in the NW Mediterranean Sea Explored by Pyrosequencing of the 16S Rrna
    Vol. 61: 221–233, 2010 AQUATIC MICROBIAL ECOLOGY Published online December 30 doi: 10.3354/ame01484 Aquat Microb Ecol Contribution to AME Special 4 ‘Progress and perspectives in aquatic microbial ecology’ OPENPEN ACCESSCCESS Spatial patterns of bacterial richness and evenness in the NW Mediterranean Sea explored by pyrosequencing of the 16S rRNA Thomas Pommier1, 2, P. R. Neal3, Josep M. Gasol1, Montserrat Coll1, Silvia G. Acinas1, Carlos Pedrós-Alió1,* 1Departament de Biologia Marina i Oceanografia, Institut de Ciències del Mar, CSIC, 08003 Barcelona, Spain 2Ecologie Microbienne, UMR5557, USC1193 CNRS, INRA, Université Lyon I, 69622 Villeurbanne, France 3Marine Biological Laboratory, Woods Hole, 02543 Massachusetts, USA ABSTRACT: Due to analytical limitations, patterns of richness and evenness of microbes are scarce in the current literature. The newest and powerful pyrosequencing technology may solve this issue by sampling thousands of sequences from the same community. We conducted a study of diversity along a horizontal transect (ca. 120 km) and a depth profile (surface to bottom at ca. 2000 m) in the northwestern Mediterranean Sea, using this technology on the V6 region of the 16S rDNA gene and analyzed patterns of richness and evenness of marine free-living bacterial communities. A total of 201 605 tag sequences were obtained from the 10 samples considered and clustered according to their similarity in 1200 operational taxonomic units (OTUs) per sample on average. We found a par- allel decrease in richness and evenness from coast to offshore and from bottom to surface. We also observed a predominance of a few OTUs in each sample, while ca. 50% of all OTUs were found as singletons, which indicated that the community structures differed dramatically between sites despite the relative proximity and the physical connectivity between the samples.
    [Show full text]
  • The Use of Entropy to Measure Structural Diversity
    The use of entropy to measure structural diversity L. Masisi 1, V. Nelwamondo 2 and T. Marwala 1 1School of Electrical & Information Engineering Witwatersrand University, P/Bag 3, Wits, 2050, South Africa 2Graduate School of Arts and Sciences, Harvard University, GSAS Mail Center Child 412, 26 Everett Street Cambridge, Massachusetts, 02138 USA Abstract — In this paper entropy based methods are accuracy. However this study will only focus on three compared and used to measure structural diversity of an measures of diversity, Shannon, Simpson and Berger ensemble of 21 classifiers. This measure is mostly applied in Parker to quantify structural diversity of the classifiers. ecology, whereby species counts are used as a measure of Shannon entropy has found its fame in information diversity. The measures used were Shannon entropy, theory as it is used to measure the uncertainty of Simpsons and the Berger Parker diversity indexes. As the states[10]. In ecology Shannon is used to measure the diversity indexes increased so did the accuracy of the ensemble. An ensemble dominated by classifiers with the diversity indices of species, however in this study instead same structure produced poor accuracy. Uncertainty rule of the biological species the individual classifiers are from information theory was also used to further define treated as species [11]. For example, if there are three diversity. Genetic algorithms were used to find the optimal species of different kind, two of the same kind and one of ensemble by using the diversity indices as the cost function. another kind, then that would replicate three MLP's of The method of voting was used to aggregate the decisions.
    [Show full text]
  • Measuring Biological Diversity in R
    Measuring biological diversity in R Dan Flynn, Brenda Lin, and Daniel Bunker 18 March 2008 Columbia University Understanding biodiversity and the ecosystem processes that come with said biodiversity can help inform policy toward sustainable development. Land use changes have affected the habitat and feeding resources of many taxa, thereby changing species composition and abundances. This change in land use and species distribution may also lead to changes in ecosystem services and functions that are necessary for human well-being. In this lab, we will look at changes within bird species diversity as land is converted from forest to more intensive coffee agriculture. Coffee is a crop that is grown within a large variation of shade cover. On the one extreme is traditional rustic coffee, which is planted under a forest canopy, and on the other extreme is intensive coffee agriculture, which has little or no shade cover (Figure 1). There is a large range of shade systems in between these two extremes. The conversion of coffee farms from traditional rustic systems to intensive, unshaded monocultures is presumed to have large effects on bird biodiversity because of the loss of vegetation diversity and structure in sun monocultures. This may be especially important for bird migration between North and South America because shade trees within traditional coffee farms have served as potential sources of habitat and food during previous migration, and declines in certain bird species have been blamed on the gradual removal of shade trees in Central American coffee systems. 1 The data you will be using in this lab looks at the bird species found in forest, rustic coffee, polyculture, and shaded monoculture habitats.
    [Show full text]
  • The PD Phylogenetic Diversity Framework: Linking Evolutionary History to Feature Diversity for Biodiversity Conservation
    CORE Metadata, citation and similar papers at core.ac.uk Provided by Springer - Publisher Connector The PD Phylogenetic Diversity Framework: Linking Evolutionary History to Feature Diversity for Biodiversity Conservation Daniel P. Faith Abstract Feature diversity refers to the relative number of different features repre- sented among species or other taxa. As a storehouse of possible future benefi ts to people, it is an important focus for biodiversity conservation. The PD phylogenetic diversity measure provides a way to measure biodiversity at the level of features. PD assumes an evolutionary model in which shared features are explained by shared ancestry. This avoids philosophical and practical weaknesses of the conventional interpretation of biodiversity as based on some measure of pair-wise differences among taxa. The link to features also provides a family of PD-based calculations that can be interpreted as if we are counting-up features of taxa. The range of feature diversity calculations assists comparisons of methods, and helps overcome the cur- rent lack of review and synthesis of the variety of proposed methods for integrating evolutionary history into biodiversity conservation. One family of popular indices is based on the evolutionary distinctiveness (ED) measure. These indices all have the limitation that complementarity, refl ecting degree of phylogenetic overlap among taxa, is not properly taken into account. Related indices provide priorities or other scores for geographic areas, but do not effectively combine complementarity, prob- abilities of extinction, and measures of restricted-range. PD-based measures can overcome these problems. Applications include the identifi cation of key biodiver- sity sites of global signifi cance for biodiversity conservation.
    [Show full text]
  • Biodiversity Accounting
    Biodiversity Accounting November 2018 Outline • Learning objectives • Key concepts • Policy linkages • Exercise • How to compile • Data sources • Country examples SEEA EEA accounts, tools and linkages 3 Biodiversity accounting : key concepts 4 What is biodiversity? Convention on Biological Diversity (CBD), 1992 defines biodiversity as: “Biological diversity means the variability among living organisms from all sources including, inter alia, terrestrial, marine and other aquatic ecosystems and the ecological complexes of which they are part; this includes diversity within species, between species and of ecosystems” 5 Biodiversity in the SEEA-EEA • Three components to biodiversity: Biodiversity Extent (or species) account account Outside of SEEA EEA • …the measurement of biodiversity is focused on the assessment of diversity of species, although changes in the diversity of ecosystems is also an important output, derived from the measurement of changes in ecosystem extent and condition. (SEEA EEA, p 152). 6 Link to SEEA EEA • In SEEA EEA: biodiversity is a characteristic relevant in measurement of condition of ecosystem assets. > Measures of biodiversity are considered to relate primarily to ecosystem assets in the accounting model. > E.g. birdwatching or fishing not seen as flows of biodiversity services > Consistent with a view that biodiversity can be degraded or enhanced over time, an attribute that applies only to assets in an accounting context. • Measures of biodiversity can be indicators of flows of final ecosystem services (e.g. biodiversity indicators related to value of recreational services from wildlife related activities, where people gain benefit from experiencing the diversity of nature (as distinct from services received from appreciation of individual species) Concepts • Species population: The summation of all the organisms of the same species or species group that live in a particular geographical area and have the capability of interbreeding.
    [Show full text]
  • Biodiversity Indexes: Value and Evaluation Purposes
    E3S Web of Conferences 48, 01001 (2018) https://doi.org/10.1051/e3sconf/20184801001 IWGM 2018 Biodiversity Indexes: Value and Evaluation Purposes Jatna Supriatna1 1Institute for Sustainable Earth and Resources (I-SER) and Dept of Biology, Faculty of Math and Sciences, Universitas Indonesia Abstract. Biodiversity is a word recently introduced by experts in the field of biology. This word became more meaningful after Edward O. Wilson of Harvard University introduced it in a book entitled Biodiversity, an extension of biological diversity, in 1989 [11]. In subsequent developments, it became very popular and used not only by environmental biologists but also by researchers, environmentalists, funders, educators, social experts, economists, policy makers, and many others, although many do not know what that means. Biodiversity includes variations within the biological community, where living species, and ecosystems, where communities are located, as well as interaction between them (Pri. The science of biodiversity has emerged rapidly since then included monitoring and evaluation systems which is measuring the value of biodiversity components, such as the number of species present, the population of species, a habitat or the sum of all such components within a given area or site. Such monitoring and evaluation may be carried out for a variety of reasons, included identification of a given area for biodiversity richness, evenness or healthy ecosystems. The richness is the number of species per sample, the more species present in a sample, the richer the sample. Evenness is a measure of the relative abundance of the different species making up the richness of an area. Two commonly used to measure biodiversity Simpson index Ds and Shannon’s index H’.
    [Show full text]
  • Community Diversity: Controls and Patterns
    Community Diversity: Controls and Patterns Topics • What is biodiversity and why is it important? • What are the major drivers of species richness? • How might the drivers of species richness and hence levels of species richness differ among biomes? Patterns of Biodiversity across Biomes Predicted Species Richness Wet Tropical Temp. Dec. Temp. Con. Boreal Desert Community Diversity Defined Biodiversity Merriam-Webster - the existence of many different kinds of plants and animals in an environment. Wikipedia - is the degree of variation of life forms within a given species, ecosystem, biome, or an entire planet. U.S. Congress Office of Technology Assessment - the variety and variability among living organisms and the ecological complexes in which they occur. Diversity can be defined as the number of different items and their relative frequency. For biological diversity, these items are organized at many levels, ranging from complete ecosystems to the chemical structures that are the molecular basis of heredity. Thus, the term encompasses different ecosystems, species, genes, and their relative abundance." Community Diversity Defined Species richness - Species evenness - Species diversity - Community Diversity Defined Species richness - number of species present in the community (without regard for their abundance). Species evenness - relative abundance of the species that are present. Species diversity - Considers both the number of species (richness) in the community and their relative abundance (evenness or equability). Shannon-Wiener Diversity Index Where: H’ = the value of the Shannon-Wiener diversity index pi = the proportion of the ith species loge = the natural logarithm s = the number of species in the community Community Diversity Defined Community Richness Shannon’s index Abundance Guild – group of species that make their living in a similar way Richness Shannon’s index Abundance Individual species Abundance Copyright © The McGraw-Hill Companies, Inc.
    [Show full text]
  • Species Diversity
    SPECIES DIVERSITY Studies of species diversity are a major component of community ecology and biogeography. Patterns of species diversity in time and space form the basis of many important ecological models, including mechanisms of succession (Con- nell and Slatyer 1977), explanations for latitudinal diversity gradients (Pianka 1966; Stevens 1989), hypotheses of mass extinction in the fossil record (Raup et al. 1973), and relationships between diversity and stability (May 1973; Goodman 1975). Measures of species diversity are often used to evaluate the success of nature reserves in preventing extinction (Soul6 and Wilcox 198O), and to assay the effects of environmental pollution on the "well-being" of natural ecosystems (Tomascik and Sander 1987). SPECIES DIVERSITY Unfortunately, "species diversity" has taken on a variety of confusing mean- ings (Hurlbert 1971). Here, we define diversity as a measure of both the number of species in the community and their relative abundances (Margalef 1968; Washington 1984). Diverse communities are characterized by a large number of species and/or a relatively even distribution of species abundances (Lambshead et al. 1983). Considerable effort has been expended to devise a single numerical index that measures these two properties (see reviews by Peet 1974; Washington 1984; Magurran 1988). Regardless of the mathematics of the index, all diversity indices incorporate three important assumptions (Peet 1974): 1. All individuals assigned to a specific class are assumed to he equal. Most diversity indices do not recognize intraspecific dif- ferences among individuals, even though age- and size-structured populations may have important community-level effects (Polis et al. 1989). In theory, ages, sexes, or size classes could be 22 Chapter 2 treated as different "species" (Hendrickson and Ehrlich 1971), but their numerical dependence on one another is different from their dependence on other species.
    [Show full text]